What is the derivative of cos^3(5x) ?

The derivative of cos^3(5x) is -15cos^2(5x)sin(5x)

What is the first derivative of cos^3(5x) ?

The first derivative of cos^3(5x) is -15cos^2(5x)sin(5x)

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\frac{d}{d x} (cos^{3} (5 x))

- 15 cos^{2} (5 x) sin (5 x)

Solution steps

\frac{d}{d x} (cos^{3} (5 x))

Apply the chain rule:

3 (cos (5 x))^{2} \frac{d}{d x} (cos (5 x))

= 3 (cos (5 x))^{2} \frac{d}{d x} (cos (5 x))

\frac{d}{d x} (cos (5 x)) = - sin (5 x) \cdot 5

= 3 (cos (5 x))^{2} (- sin (5 x) \cdot 5)

Simplify

= - 15 cos^{2} (5 x) sin (5 x)

\int_{0}^{1} \frac{2 t}{( 2 - t ) ^{2}} d t

\int \frac{x ^{3}}{x ^{2} - 9} d x

\frac{9}{( 1 - x ) ^{2}}

n = 1 \sum \infty \frac{1}{n ^{5}}

f (x) = (12 - x) 24 x - 144

What is the derivative of cos^3(5x) ?
The derivative of cos^3(5x) is -15cos^2(5x)sin(5x)
What is the first derivative of cos^3(5x) ?
The first derivative of cos^3(5x) is -15cos^2(5x)sin(5x)